PID ALGORITHM and TUNING METHODS John A. Shaw Process Control Solutions Rochester, New York 585-234-5864 The PID control algorithm is used for the control of almost all loops in the process industries, and is also the basis for many advanced control algorithms and strategies. In order for control loops to work properly, the PID loop must be properly tuned. Standard methods for tuning loops and criteria for judging the loop tuning have been used for many years, but should be reevaluated for use on modern digital control systems. While the basic algorithm has been unchanged for many years and is used in all distributed control systems, the actual digital implementation of the algorithm has changed and differs from one system to another and from commercial equipment to academia. We will discuss controller tuning methods and criteria. Also discussed will be the digital PID control algorithm, how it works, the various implementation methods and options, and how these affect the operation and tuning of the controller. Chapter 1 The Feedback Control Loop The system measures the process, compares it to a setpoint, and then manipulates the output in the direction which should move the process toward the setpoint. Valve Linearity Valves are usually non-linear. That is, the flow through the valve is not the same as the valve position. Several types of valves exist: Linear Same gain regardless of valve position Equal Percentage Low gain when valve is nearly closed High gain when valve is nearly open Quick Opening High gain when valve is nearly closed Low gain when valve is nearly open As we will see later, the gain of the process, including the valve, is very important to the tuning of the loop. • If the controller is tuned for one process gain, it may not work for other process gains. Valve Linearity: Installed characteristics The flow vs. percent open curve changes due to the head loss in the piping At low flow, the head loss through the pipes is less , leaving a larger differential pressure across the valve. At high flow, the head loss through the pipe is more, leaving a smaller differential pressure across the valve. The effect is to increase the non-linearity of most valves. Fail Open Valves Valves are usually either: Fail Closed, air to open or Fail Open, air to close • Regardless of the way the valve operates, the operator is interested in the knowing and adjusting the position of the valve, not the value of the signal. "Up is always open" • All controllers have some means of indicating the controller output in terms of the valve position. When the operator increases the output as indicated on the controller, the valve opens. Indication Inversion The output indication is inverted. The controller action takes the valve action into acount. The flow loop is direct acting. Most analog controllers work like this. Signal Inversion The output signal is inverted. The controller action ignores the valve action. The flow loop is reverse acting Some distributed control systems work like this. Chapter 2 The Process Response to the Controller Steady state relationships: Relating valve change to measurement change Steady state relationships: changing load When the load changes, either the process value changes or the valve position must be changed to compensate for the load change. Process Dynamics: Simple lag [...]... feedback (process measurement) to perform The PID algorithm must be "tuned" for the particular process loop Without such tuning, it will not be able to function • To be able to tune a PID loop, each of the terms of the PID equation must be understood • The tuning is based on the dynamics of the process response The PID Control Algorithm The PID control algorithm comprises three elements: • Proportional... Elementary methods 1 The plant didn’t blow up 2 The process measurements stay close enough to the setpoint 3 They say it’s OK and you can go home now Informal methods 1 Optimum decay ratio (1/4 wave decay) 2 Minimum overshoot 3 Maximum disturbance rejection The choice of methods depends upon the loop’s place in the process and its relationship with other loops Mathematical criteria Mathematical methods minimization... relationship between the setpoint, the measurement, and the output Proportional—units The proportional or gain term may be calibrated in two ways: Gain and Proportional Band Gain = Output/Input Increasing the gain will cause the output to move more Proportional band is the % change in the input which would result in a 100% change in the output Proportional Band = 100/Gain We will use gain in this document... Automatic Reset or simply Reset • Derivative • - also known as Rate or Pre-Act (TM of Taylor Instrument Co.) The algorithm is normally available in several combinations of these elements: • Proportional only Proportional and Integral (most common) • Proportional, Integral, and Derivative • Proportional and Derivative • We will examine each of the three elements below: Proportional E = Measurement - Setpoint... Mode: The control algorithm manipulates the output to hold the process measurements at their setpoints This should be the most common mode for normal operation Key concepts The PID control algorithm does not "know" the correct output to bring the process to the setpoint • It merely continues to move the output in the direction which should move the process toward the setpoint • The algorithm must have... Where G = Gain R = Reset (repeats per minute) D = Derivative (minutes) Note: See Interactive vs Noninteractive (below) Chapter 4 Additional PID Concepts Interactive or Noninteractive algorithm "Interactive" and "Noninteractive" refer to interaction between the reset and derivative terms This is also known as "series" or "parallel" derivative Almost all analog controllers are interactive Many digital controllers... be measured Chapter 3 The PID algorithm Action PROCESS ACTION Defines the relationship between changes in the valve and changes in the measurement DIRECT measurement Increase in valve position causes an increase in the REVERSE Increase in valve position causes a decrease in the measurement CONTROLLER ACTION Defines the relationship between changes in the measured variable and changes in the controller... Integral of time times error squared: • These mathematical methods are used primarily for academic purposes, together with process simulations, in the study of control algorithms On-line trial tuning or The "by-guess- and- by- golly" method 1 Enter an initial set of tuning constants from experience A conservative setting would be a gain of 1 or less and a reset of less than 0.1 2 Put loop in automatic with... the intercept of tangent line and original process value The gain, reset, and Derivative are calculated using: Gain P X/DR Reset Derivative — — 0.3/D PI 0.9X/DR — 0.5/D PID 1.2X/DR 0.5D Ziegler Nichols tuning method: open loop point of inflection Another means of determining parameters based on the ZN open loop After "bumping" the output, watch for the point of inflection and note: Ti min Time from output... the reset setting in repeats per minute Units used to set integral or reset Assume a controller with proportional and integral only Calculation of repeat time: (gain and reset terms used in controller) With the error set to zero (measurement input = setpoint), make a change in the input and note the immediate change in output The output will continue to change (it is integrating the error) Note the